zenpundit.com » mathematics

Archive for the ‘mathematics’ Category

A couple or so couples

Saturday, February 18th, 2017

[ by Charles Cameron — gathering these things the way an obsessed squirrel gathers nuts ]

I’d say there’s nothing more thought-provocative than running across an unexpected parallelism or opposition — and the closer the parallel the better. Once thought has been provoked, though that’s just the starting point — it needs to run its course with the appropriate caution and rigor. Here, then, are some parallelisms I’ve run into recently, for your provocation.


The Dilletante’s Winterings, Michael McFaul’s easy, broken parallel:

Michael McFaul, the former US ambassador to Russia, has a blog on the site of Ekho Moskvy, the independent radio station based in Moscow. Commenting on the appointment of Steve Bannon to the National Security Council, he wrote:

It’s the equivalent of Putin appointing Alexander Dugin to the [Russian] Security Council and telling generals Bortnikov [head of the FSB] and Gerasimov [head of the general staff] to only attend when they are needed.


Craig Whiteside (2016) The Islamic State and the Return of RevolutionaryWarfare, Small Wars & Insurgencies, 27:5, 743-776, DOI: 10.1080/09592318.2016.1208287:

This paper starts by comparing the Islamic State to the Vietnamese communists in a revolutionary warfare framework..

I didn’t find a single-sentence assertion of this parallelism, not am I expert in revolutionary warfare — but manynof our readers here on Zenpundit are, so I’ll leave the critical appraisal of this proposition to you-all..


Defense One, So, American Mass Shooters and Islamic Terrorists Do Have Something in Common:

Like radical Islamic groups, white supremacist and other right-wing terrorist groups offer people (especially men) who feel isolated and disempowered a chance to feel important and welcome. It’s the same psychological phenomenon, different culture war. And thus the KKK gains new recruits along with ISIL.


And for good measure… not, you understand, that I understand it —

Metod Saniga, Algebraic Geometry: a Tool for Resolving the Enigma of Time?

An illustrative example of such a temporal dimension is provided by a specific linear, single-parametric set (so-called pencil) of conics in the projective plane. This set of conics is found to nicely reproduce the experienced arrow of time when the projective plane is affinized; it simply suffices to postulate that each proper conic of the pencil stands for a single temporal event, and relate three distinct kinds of (proper) affine conic, viz. a hyperbola, a parabola and an ellipse, with the three different kinds of temporal event, viz. the past, present and future, respectively..

Time, as St Augustine noted, makes sense — until you try to figure out what sense it makes.

It’s easier to accept John Nash than the goddess Namagiri

Saturday, January 7th, 2017

[ by Charles Cameron — delighted to find Ramanujan is not alone in dreaming of mathematics ]

When the Hinduism Today writer above says people found Ramanujan‘s assertion that his equations were given him in dreams by the local goddess Namagiri “irksome” he was understing the case: many mathematicians are allergic to the idea of a goddess providing inspiration to a mathematician in a devotional dream state. Thus Krishnaswami Alladi, in his Review of the Movie on the mathematical genius Ramanujan, writes:

The legend is that the Hindu Goddess Namagiri came in Ramanujan’s dreams and gave him these formulae..

See? It’s a legend, a priori, since “goddesses” don’t exist.

John Nash, he of the Beautiful Mind, game theory equilibria, and the Nobel Prize, on the other hand — if he provides inspiration to a fellow mathematician in a dream?

Why, his solution can be acknowledged as such in a learned paper..

Coffee & Donuts, a topological DoubleQuote

Monday, October 10th, 2016

[ by Charles Cameron — sadly, now dunkin’ diabetes ]

Some might claim that Dunkin is the link between Coffee and Donuts — it’s certainly a link I’ve appreciated myself on more than one occasion. Here’s another, and arguably more subtle linkage — topology.

In verbal format, it’s a mathematician’s inside joke:

The joke goes about topologists is that they can’t tell the difference between a coffee mug and a doughnut. For those who are not familiar with topology, topology is the study of geometrical objects where you don’t care about lengths and you don’t care about angles, what matters is how the spatial relations relate to each other.

Even better, here’s the same joke, illustrated — or refuted, if you prefer — in video by a master maker:

The only problem here — it’ll all prove a little pointless if you dunk your donut into the coffee cup without first supplying some coffee..

But morphing! What an ingenious way to provide and prove a DoubleQuote!

On the felicities of graph-based game-board design: nine

Sunday, October 9th, 2016

[ by Charles Cameron — if the territory is graphical, so’s the map ]

Terrain, with its named places and transportation links between them, is graphical, as illustrated in this map:

It makes me wonder how often graph theory (of the sort that gives us the Königsberg Bridge Problem, see the first post in this series) is applied to troop movements — as it often is to public transportation (see the upcoming tenth post).


My next example of the use of a node-and-edge graphical design both puzzles and intrigues me:

It puzzles me, because I can’t quitec grasp what Raza Rumi — a very bright fellow — is up to in choosing this particular illustration. And it intrigues me, because once on a vision quest I glimpsed an outstretched eagle’s or hawk’s wing, with a similar graphical overlay of its structural essence. It’s a sight I’ve never forgotten, an exquisite linking of the real and abstract worlds, and one that I’m sadly ill-equipped to reproduce visually myself. Words don’t do it justice.


My third example, as you can see, is taken from a learned paper describing the use of graphs to illustrate musical compositions according to a strictly defined protocol:

What interests me here — aside from the fact that any of these digrams could be used as a board in a sufficiently complex HipBone or Sembl game — is that I ran across this particular paper within 24 hours of reading m’friend Bill Benzon‘s account of his friend Michael Bérubé and his son Jamie, introduced in this tweet:

Bill’s post Jamie’s Investigations, Part 1: Emergence to which his tweet refers us — is illustrated thus:


Michael Bérubé, we read, has recently published a book about Jamie, who has Down’s, Life as Jamie Knows It: An Exceptional Child Grows Up, and it contains a series of Jamie’s drawings, of which this is one example.

Bill, who is himself the author of Beethoven’s Anvil: Music in Mind and Culture, notes “Jamie loves music, and his dad is a rock-and-roll drummer, so’s his older brother Nick, I believe.” And here’s the clincher — he then asks:

In what way are these drawings like drum beats?

So that’s two examples of novel visual representations of musical pattern in just two days, earlier this week.


Enough for now — onwards to On the felicities of graph-based game-board design: ten — a long, fascinating post IMO, long enough that I’m glad this is a Sunday.

Earlier in this series:

  • On the felicities of graph-based game-board design: preliminaries
  • On the felicities of graph-based game-board design: two dazzlers
  • On the felicities of graph-based game-board design: three
  • On the felicities of graph-based game-board design: four
  • On the felicities of graph-based game-board design: five
  • On the felicities of graph-based game-board design: six
  • On the felicities of graph-based game-board design: seven
  • On the felicities of graph-based game-board design: eight
  • On play as wildness

    Saturday, September 24th, 2016

    [ by Charles Cameron — what’s true of hex maps is true of all mental models ]

    There’s a certain let-your-hair-down quality to play.

    It appears that one Tausendsassa Friedensreich Regentag Dunkelbunt Hundertwasser said or perhaps wrote, muttered, whispered, shouted, or simply thought out loud, “the straight line is a godless line” — at any rate, someone noticed and recorded the phrase, and now it’s scattered across the net and difficult to track to its source.


    But we do love order, don’t we?


    And so the rivers on our hexagonal maps all too easily follow the hexagons..


    when they’d more realistically cross over them, following their own courses:


    and note how easily even our efforts to bring natural variety to our hexagonal mappings conform more to hexagons than to variety.



    Zennist Thich Nhat Hanh in Listening Deeply for Peace writes:

    A traditional Vietnamese Zen garden is very different from a Japanese Zen garden. Our Zen gardens, called hon non bo, are wild and exuberant, more playful than the formal Japanese gardens with their restrained patterns. Vietnamese Zen gardens are seriously unserious. For us, the whole world is contained in this peaceful place. All activities of life unfold in true peace in the garden: in one part, children will be playing, and in another part, some elderly men will be having a chess game; couples are walking; families are having picnics; animals are free to wander around. Beautiful trees are growing next to abundant grasses and flowers. There is water, and there are rock formations. All ecologies are represented in this one microecology without discrimination. It is a miniature, peaceful world. It is a beautiful living metaphor for what a new global ethic could bring.


    Here is the wrestling of a tree with such angels as gravity, sun, wind and rain:


    Here is the wild calligraphy of the Rio Mamoré across the forests of the Amazon basin:


    Switch to our mobile site